Question: Solve for $x$ and $y$ using elimination. ${-2x-3y = -32}$ ${-3x-5y = -53}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $-3$ ${-10x-15y = -160}$ $9x+15y = 159$ Add the top and bottom equations together. $-x = -1$ $\dfrac{-x}{{-1}} = \dfrac{-1}{{-1}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {-2x-3y = -32}\thinspace$ to find $y$ ${-2}{(1)}{ - 3y = -32}$ $-2-3y = -32$ $-2{+2} - 3y = -32{+2}$ $-3y = -30$ $\dfrac{-3y}{{-3}} = \dfrac{-30}{{-3}}$ ${y = 10}$ You can also plug ${x = 1}$ into $\thinspace {-3x-5y = -53}\thinspace$ and get the same answer for $y$ : ${-3}{(1)}{ - 5y = -53}$ ${y = 10}$